So much by way of arguing that we are not bound to hold that all relational properties are internal in the particular sense, with which we are now concerned, in which to say that they are means that in every case in which a thing A has a relational property, it follows from the proposition that a term has _not_ got that property that the term in question is _other_ than A. But I have gone further and asserted that some relational properties certainly are _not_ internal. And in defence of this proposition I do not know that I have anything to say but that it seems to me evident in many cases that a term which _has_ a certain relational property _might_ quite well not have had it: that, for instance, from the mere proposition that this is this, it by no means follows that this has to other things all the relations which it in fact has. Everybody, of course, must admit that if all the propositions which assert of it that it has these properties, do in fact follow from the proposition that this is this, we cannot see that they do. And so far as I can see, there is no reason of any kind for asserting that they do, except the confusion which I have exposed. But it seems to me further that we can see in many cases that the proposition that this has that relation does _not_ follow from the fact that it is this: that, for instance, the proposition that Edward VII was father of George V _is_ a _mere_ matter of fact.
I want now to return for a moment to that other meaning of "internal," (p. 286) in which to say that P is internal to A means not merely that anything which had not P would necessarily be _other_ than A, but that it would necessarily be _qualitatively_ different. I said that this was the meaning of "internal" in which the dogma of internal relations holds that all relational properties are "internal"; and that one of the most important consequences which followed from it, was that all relational properties are "internal" in the less extreme sense that we have just been considering. But, if I am not mistaken, there is another important consequence which also follows from it, namely, the Identity of Indiscernibles. For if it be true, in the case of every relational property, that any term which had net that property would necessarily be qualitatively different from any which had, it follows of course that, in the case of two terms one of which has a relational property, which the other has not the two are qualitatively different. But, from the proposition that _x_ is other than _y,_ it _does_ follow that _x_ has some relational property which _y_ has not; and hence, if the dogma of internal relations be true, it will follow that if _x_ is other than _y, x_ is always also qualitatively different from _y,_ which is the principle of Identity of Indiscernibles. This is, of course, a further objection to the dogma of internal relations, since I think it is obvious that the principle of Identity of Indiscernibles is not true. Indeed, so far as I can see, the dogma of internal relations essentially consists in the joint assertion of two indefensible propositions: (1) the proposition that in the case of no relational property is it true of any term which has got that property, that it _might_ not have had it and (2) the Identity of Indiscernibles.